The invention relates to a measuring device for contact-free measuring of a rotation angle and/or torque of a shaft. In a known measuring device, the torque can be measured at the shaft by means of two cylindrical sleeves which are concentric to one another and to the shaft axis, rotatable relative to one another and divided at their circumferential surface into an equal number of a plurality of segment-like outer surface areas which are parallel to the shaft axis. The outer surface areas have high and low electrical conductivity alternating in the circumferential direction and are enclosed by at least one winding which is coaxial to the sleeves.